Fourier Number Using Biot Number Calculator

Fourier Number Formula:

\[ Fo = \frac{-1}{Bi} \cdot \ln\left(\frac{T - T_{\infty}}{T_0 - T_{\infty}}\right) \]

Biot Number (Bi):

Temperature at Any Time T (T):

Temperature of Bulk Fluid (T∞):

Initial Temperature of Object (T₀):

Fourier Number (Fo):

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1. What is Fourier Number?

The Fourier Number is a dimensionless quantity that represents the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter. It's commonly used in heat transfer and mass transfer analysis.

2. How Does the Calculator Work?

The calculator uses the Fourier Number formula:

\[ Fo = \frac{-1}{Bi} \cdot \ln\left(\frac{T - T_{\infty}}{T_0 - T_{\infty}}\right) \]

Where:

\( Fo \) — Fourier Number (dimensionless)
\( Bi \) — Biot Number (dimensionless)
\( T \) — Temperature at Any Time T (K)
\( T_{\infty} \) — Temperature of Bulk Fluid (K)
\( T_0 \) — Initial Temperature of Object (K)
\( \ln \) — Natural logarithm function

Explanation: This formula calculates the Fourier Number using the Biot Number and temperature values at different states.

3. Importance of Fourier Number Calculation

Details: The Fourier Number is crucial in transient heat conduction analysis. It helps determine how quickly a system responds to temperature changes and is used to characterize the time scale of thermal diffusion processes.

4. Using the Calculator

Tips: Enter Biot Number (must be positive), temperature values in Kelvin. Ensure that T₀ - T∞ is not zero to avoid division by zero errors.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Fourier Number?
A: Fourier Number represents the ratio of heat conduction rate to heat storage rate. A higher Fo indicates faster thermal response.

Q2: How is Fourier Number related to Biot Number?
A: Both are dimensionless numbers used in heat transfer. Biot Number relates internal conduction resistance to surface convection resistance, while Fourier Number relates conduction rate to storage rate.

Q3: What are typical values for Fourier Number?
A: Fourier Number typically ranges from 0 to large values, depending on the time scale and thermal properties of the material.

Q4: When is this formula applicable?
A: This formula is used for transient heat conduction problems with constant boundary conditions and uniform initial temperature.

Q5: What are the limitations of this calculation?
A: The formula assumes constant thermal properties, uniform initial temperature, and constant fluid temperature. It may not be accurate for complex geometries or varying boundary conditions.